Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).

[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).

[Crossref]

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).

[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).

[Crossref]

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).

[Crossref]

X. Chen, M. Mohamed, Z. Li, L. Shang, and A. R. Mickelson, “Process variation in silicon photonic devices,” Appl. Opt. 52, 7638–7647 (2013).

[Crossref]
[PubMed]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).

[Crossref]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).

[Crossref]

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).

[Crossref]

M. S. Eldred, “Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design,” AIAA Paper 2274, 37 (2009).

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).

[Crossref]

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).

[Crossref]

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).

[Crossref]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).

[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).

[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).

[Crossref]

P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.

D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).

[Crossref]
[PubMed]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).

[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).

[Crossref]

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).

[Crossref]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).

[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

M. S. Eldred, “Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design,” AIAA Paper 2274, 37 (2009).

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).

[Crossref]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).

[Crossref]

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).

[Crossref]

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).

[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).

[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).

[Crossref]

D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).

[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).

[Crossref]

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).

[Crossref]

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).

[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).

[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach Optical Filter Design and Analysis: A Signal Processing Approach (Wiley Online Library, 1999).

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).

[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).

[Crossref]

P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).

[Crossref]

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).

[Crossref]

A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).

[Crossref]

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).

[Crossref]
[PubMed]

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).

[Crossref]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for wdm systems,” J. Lightwave Technol. 20, 296–303 (2002).

[Crossref]

D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.

A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).

[Crossref]

D. Cassano, F. Morichetti, and A. Melloni, “Statistical analysis of photonic integrated circuits via polynomial-chaos expansion,” in “Signal Processing in Photonic Communications,” (Optical Society of America, 2013), pp. JT3A–8.

A. Papoulis, “Random variables and stochastic processes,” (McGraw-Hill, 1985).

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.

J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.

J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.

J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).

[Crossref]

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).

[Crossref]

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).

[Crossref]

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).

[Crossref]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).

[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

P. Manfredi, I. S. Stievano, and F. G. Canavero, “Parameters variability effects on microstrip interconnects via hermite polynomial chaos,” in “Proc. of the 19th Conference on Electrical Performance of Electronic Packaging and Systems,” (2010), pp. 149–152.

J. B. Preibisch, P. Triverio, and C. Schuster, “Design space exploration for printed circuit board vias using polynomial chaos expansion,” in “Electromagnetic Compatibility (EMC), 2016 IEEE International Symposium on,” (IEEE, 2016), pp. 812–817.

J. B. Preibisch, P. Triverio, and C. Schuster, “Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables,” in “Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 2015 IEEE MTT-S International Conference on,” (IEEE, 2015), pp. 1–4.

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).

[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).

[Crossref]

A. Waqas, D. Melati, and A. Melloni, “Stochastic simulation and sensitivity analysis of photonic circuit through morris and sobol method,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2017,” (IEEE, 2017), pp. 1–3.

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).

[Crossref]
[PubMed]

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).

[Crossref]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).

[Crossref]

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).

[Crossref]

D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).

[Crossref]

D. Xiu, Numerical methods for stochastic computations: a spectral method approach (Princeton University Press, 2010).

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).

[Crossref]

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).

[Crossref]
[PubMed]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).

[Crossref]

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach Optical Filter Design and Analysis: A Signal Processing Approach (Wiley Online Library, 1999).

P. Sochala and O. Le Maître, “Polynomial chaos expansion for subsurface flows with uncertain soil parameters,” Adv. Water Resources 62, 139–154 (2013).

[Crossref]

M. S. Eldred, “Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design,” AIAA Paper 2274, 37 (2009).

X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented cad-tool for simulating complex integrated optical circuits,” IEEE J. Sel. Top. Quantum Electron. 2, 257–262 (1996).

[Crossref]

P. Manfredi, D. V. Ginste, D. De Zutter, and F. G. Canavero, “Uncertainty assessment of lossy and dispersive lines in spice-type environments,” IEEE Trans. Components Packaging Manufacturing Technol. 3, 1252–1258 (2013).

[Crossref]

Z. Zhang, T. A. El-Moselhy, I. M. Elfadel, and L. Daniel, “Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos,” IEEE Trans. Computer-Aided Design Integrated Circuits Systems 32, 1533–1545 (2013).

[Crossref]

Y. Ye, D. Spina, P. Manfredi, D. V. Ginste, and T. Dhaene, “A comprehensive and modular stochastic modeling framework for the variability-aware assessment of signal integrity in high-speed links,” IEEE Trans. Electromagnetic Compatibility 60, 459–467 (2018).

[Crossref]

D. Spina, T. Dhaene, L. Knockaert, and G. Antonini, “Polynomial chaos-based macromodeling of general linear multiport systems for time-domain analysis,” IEEE Trans. Microwave Theory Techniques 65, 1422–1433 (2017).

[Crossref]

D. Spina, F. Ferranti, T. Dhaene, L. Knockaert, G. Antonini, and D. V. Ginste, “Variability analysis of multiport systems via polynomial-chaos expansion,” IEEE Trans. Microwave Theory Techniques 60, 2329–2338 (2012).

[Crossref]

D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys. 187, 137–167 (2003).

[Crossref]

D. Melati, F. Morichetti, A. Canciamilla, D. Roncelli, F. M. Soares, A. Bakker, and A. Melloni, “Validation of the building-block-based approach for the design of photonic integrated circuits,” J. Lightwave Technol. 30, 3610–3616 (2012).

[Crossref]

A. Waqas, D. Melati, and A. Melloni, “Sensitivity analysis and uncertainty mitigation of photonic integrated circuits,” J. Lightwave Technol. 35, 3713–3721 (2017).

[Crossref]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for wdm systems,” J. Lightwave Technol. 20, 296–303 (2002).

[Crossref]

M. Villegas, F. Augustin, A. Gilg, A. Hmaidi, and U. Wever, “Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties,” Math. Computers Simulation 82, 805–817 (2012).

[Crossref]

T.-W. Weng, D. Melati, A. Melloni, and L. Daniel, “Stochastic simulation and robust design optimization of integrated photonic filters,” Nanophotonics 6, 299–308 (2017).

T.-W. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, and L. Daniel, “Uncertainty quantification of silicon photonic devices with correlated and non-gaussian random parameters,” Opt. Express 23, 4242–4254 (2015).

[Crossref]
[PubMed]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).

[Crossref]
[PubMed]

Y. Xing, D. Spina, A. Li, T. Dhaene, and W. Bogaerts, “Stochastic collocation for device-level variability analysis in integrated photonics,” Photonics Res. 4, 93–100 (2016).

[Crossref]

R. Ghanem and P. D. Spanos, “A stochastic galerkin expansion for nonlinear random vibration analysis,” Probabilistic Engineering Mechanics 8, 255–264 (1993).

[Crossref]

D. Xiu and G. E. Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24, 619–644 (2002).

[Crossref]

D. Xiu, Numerical methods for stochastic computations: a spectral method approach (Princeton University Press, 2010).

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